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Simplifying -5p2 + 100p + -0.75 = 0 Reorder the terms: -0.75 + 100p + -5p2 = 0 Solving -0.75 + 100p + -5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.15 + -20p + p2 = 0 Move the constant term to the right: Add '-0.15' to each side of the equation. 0.15 + -20p + -0.15 + p2 = 0 + -0.15 Reorder the terms: 0.15 + -0.15 + -20p + p2 = 0 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + -20p + p2 = 0 + -0.15 -20p + p2 = 0 + -0.15 Combine like terms: 0 + -0.15 = -0.15 -20p + p2 = -0.15 The p term is -20p. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20p + 100 + p2 = -0.15 + 100 Reorder the terms: 100 + -20p + p2 = -0.15 + 100 Combine like terms: -0.15 + 100 = 99.85 100 + -20p + p2 = 99.85 Factor a perfect square on the left side: (p + -10)(p + -10) = 99.85 Calculate the square root of the right side: 9.992497185 Break this problem into two subproblems by setting (p + -10) equal to 9.992497185 and -9.992497185.Subproblem 1
p + -10 = 9.992497185 Simplifying p + -10 = 9.992497185 Reorder the terms: -10 + p = 9.992497185 Solving -10 + p = 9.992497185 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = 9.992497185 + 10 Combine like terms: -10 + 10 = 0 0 + p = 9.992497185 + 10 p = 9.992497185 + 10 Combine like terms: 9.992497185 + 10 = 19.992497185 p = 19.992497185 Simplifying p = 19.992497185Subproblem 2
p + -10 = -9.992497185 Simplifying p + -10 = -9.992497185 Reorder the terms: -10 + p = -9.992497185 Solving -10 + p = -9.992497185 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = -9.992497185 + 10 Combine like terms: -10 + 10 = 0 0 + p = -9.992497185 + 10 p = -9.992497185 + 10 Combine like terms: -9.992497185 + 10 = 0.007502815 p = 0.007502815 Simplifying p = 0.007502815Solution
The solution to the problem is based on the solutions from the subproblems. p = {19.992497185, 0.007502815}
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